Final answer:
To determine the combined mass of the bicycle and cyclist from the work done during acceleration, the work-energy theorem is applied, and the kinetic energy formula is used in the calculation, resulting in a combined mass of approximately 82.6 kg.
Step-by-step explanation:
The task is to calculate the combined mass of the bicycle and cyclist based on the work done to accelerate from one velocity to another. To find this, we can use the work-energy theorem, which states that the work done on an object equals the change in kinetic energy (work done = ΔKE).
Therefore, first, we convert the velocities from km/hr to m/s (10.9 km/hr = 3.028 m/s and 15.6 km/hr = 4.333 m/s). Next, we use the kinetic energy formula, KE = ½mv2, and solve for the mass (m) using the given work done (397 J).
The equation will be set up as follows:
Work done = Change in KE = ½m(vf2 - vi2)
397 J = ½m(4.333 m/s)2 - (3.028 m/s)2)
Solving this equation for m (mass) gives us:
397 J = ½m(18.774 - 9.169)
397 J = ½m * 9.605
m = (397 J) / (0.5 * 9.605 m2/s2)
m = 82.6 kg
So, the combined mass of the bicycle and the cyclist is approximately 82.6 kg.